Multivariable Linear Systems And Projective Algebraic Geometry

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Methods of Algebraic Geometry in Control Theory: Part II

Author : Peter Falb
Publisher : Springer
ISBN 13 : 3319965743
Total Pages : 390 pages
Book Rating : 4.3/5 (199 download)

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Book Synopsis Methods of Algebraic Geometry in Control Theory: Part II by : Peter Falb

Download or read book Methods of Algebraic Geometry in Control Theory: Part II written by Peter Falb and published by Springer. This book was released on 2018-09-14 with total page 390 pages. Available in PDF, EPUB and Kindle. Book excerpt: "An introduction to the ideas of algebraic geometry in the motivated context of system theory." This describes this two volume work which has been specifically written to serve the needs of researchers and students of systems, control, and applied mathematics. Without sacrificing mathematical rigor, the author makes the basic ideas of algebraic geometry accessible to engineers and applied scientists. The emphasis is on constructive methods and clarity rather than on abstraction. While familiarity with Part I is helpful, it is not essential, since a considerable amount of relevant material is included here. Part I, Scalar Linear Systems and Affine Algebraic Geometry, contains a clear presentation, with an applied flavor , of the core ideas in the algebra-geometric treatment of scalar linear system theory. Part II extends the theory to multivariable systems. After delineating limitations of the scalar theory through carefully chosen examples, the author introduces seven representations of a multivariable linear system and establishes the major results of the underlying theory. Of key importance is a clear, detailed analysis of the structure of the space of linear systems including the full set of equations defining the space. Key topics also covered are the Geometric Quotient Theorem and a highly geometric analysis of both state and output feedback. Prerequisites are the basics of linear algebra, some simple topological notions, the elementary properties of groups, rings, and fields, and a basic course in linear systems. Exercises, which are an integral part of the exposition throughout, combined with an index and extensive bibliography of related literature make this a valuable classroom tool or good self-study resource. The present, softcover reprint is designed to make this classic textbook available to a wider audience. "The exposition is extremely clear. In order to motivate the general theory, the author presents a number of examples of two or three input-, two-output systems in detail. I highly recommend this excellent book to all those interested in the interplay between control theory and algebraic geometry." —Publicationes Mathematicae, Debrecen "This book is the multivariable counterpart of Methods of Algebraic Geometry in Control Theory, Part I.... In the first volume the simpler single-input–single-output time-invariant linear systems were considered and the corresponding simpler affine algebraic geometry was used as the required prerequisite. Obviously, multivariable systems are more difficult and consequently the algebraic results are deeper and less transparent, but essential in the understanding of linear control theory.... Each chapter contains illustrative examples throughout and terminates with some exercises for further study." —Mathematical Reviews

Methods of Algebraic Geometry in Control Theory: Part I

Author : Peter Falb
Publisher : Springer
ISBN 13 : 3319980262
Total Pages : 202 pages
Book Rating : 4.3/5 (199 download)

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Book Synopsis Methods of Algebraic Geometry in Control Theory: Part I by : Peter Falb

Download or read book Methods of Algebraic Geometry in Control Theory: Part I written by Peter Falb and published by Springer. This book was released on 2018-08-25 with total page 202 pages. Available in PDF, EPUB and Kindle. Book excerpt: "An introduction to the ideas of algebraic geometry in the motivated context of system theory." Thus the author describes his textbook that has been specifically written to serve the needs of students of systems and control. Without sacrificing mathematical care, the author makes the basic ideas of algebraic geometry accessible to engineers and applied scientists. The emphasis is on constructive methods and clarity rather than abstraction. The student will find here a clear presentation with an applied flavor, of the core ideas in the algebra-geometric treatment of scalar linear system theory. The author introduces the four representations of a scalar linear system and establishes the major results of a similar theory for multivariable systems appearing in a succeeding volume (Part II: Multivariable Linear Systems and Projective Algebraic Geometry). Prerequisites are the basics of linear algebra, some simple notions from topology and the elementary properties of groups, rings, and fields, and a basic course in linear systems. Exercises are an integral part of the treatment and are used where relevant in the main body of the text. The present, softcover reprint is designed to make this classic textbook available to a wider audience. "This book is a concise development of affine algebraic geometry together with very explicit links to the applications...[and] should address a wide community of readers, among pure and applied mathematicians." —Monatshefte für Mathematik

Methods of Algebraic Geometry in Control Theory: Multivariable linear systems and projective algebraic geometry

Author : Peter L. Falb
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (9 download)

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Book Synopsis Methods of Algebraic Geometry in Control Theory: Multivariable linear systems and projective algebraic geometry by : Peter L. Falb

Download or read book Methods of Algebraic Geometry in Control Theory: Multivariable linear systems and projective algebraic geometry written by Peter L. Falb and published by . This book was released on 1990 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Methods of Algebraic Geometry in Control Theory: Part II

Author : Peter Falb
Publisher : Birkhäuser
ISBN 13 : 9780817641139
Total Pages : 408 pages
Book Rating : 4.6/5 (411 download)

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Book Synopsis Methods of Algebraic Geometry in Control Theory: Part II by : Peter Falb

Download or read book Methods of Algebraic Geometry in Control Theory: Part II written by Peter Falb and published by Birkhäuser. This book was released on 1999 with total page 408 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Control theory represents an attempt to codify, in mathematical terms, the principles and techniques used in the analysis and design of control systems. Algebraic geometry may, in an elementary way, be viewed as the study of the structure and properties of the solutions of systems of algebraic equations. The aim of this book is to provide access to the methods of algebraic geometry for engineers and applied scientists through the motivated context of control theory" .* The development which culminated with this volume began over twenty-five years ago with a series of lectures at the control group of the Lund Institute of Technology in Sweden. I have sought throughout to strive for clarity, often using constructive methods and giving several proofs of a particular result as well as many examples. The first volume dealt with the simplest control systems (i.e., single input, single output linear time-invariant systems) and with the simplest algebraic geometry (i.e., affine algebraic geometry). While this is quite satisfactory and natural for scalar systems, the study of multi-input, multi-output linear time invariant control systems requires projective algebraic geometry. Thus, this second volume deals with multi-variable linear systems and pro jective algebraic geometry. The results are deeper and less transparent, but are also quite essential to an understanding of linear control theory. A review of * From the Preface to Part 1. viii Preface the scalar theory is included along with a brief summary of affine algebraic geometry (Appendix E).

Multivariable Linear Systems and Projective Algebraic Geometry

Author : Peter Falb
Publisher :
ISBN 13 : 9783764341138
Total Pages : 390 pages
Book Rating : 4.3/5 (411 download)

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Book Synopsis Multivariable Linear Systems and Projective Algebraic Geometry by : Peter Falb

Download or read book Multivariable Linear Systems and Projective Algebraic Geometry written by Peter Falb and published by . This book was released on 1999-01-01 with total page 390 pages. Available in PDF, EPUB and Kindle. Book excerpt: Multivariable Linear Systems and Projective Algebraic Geometry.

Linear Systems Theory & Introductory Algebraic Geometry

Author : Róbert Hermann
Publisher : Math-Sci Press
ISBN 13 : 9780915692071
Total Pages : 282 pages
Book Rating : 4.6/5 (92 download)

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Book Synopsis Linear Systems Theory & Introductory Algebraic Geometry by : Róbert Hermann

Download or read book Linear Systems Theory & Introductory Algebraic Geometry written by Róbert Hermann and published by Math-Sci Press. This book was released on 1974 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Lectures on Curves, Surfaces and Projective Varieties

Author : Mauro Beltrametti
Publisher : European Mathematical Society
ISBN 13 : 9783037190647
Total Pages : 512 pages
Book Rating : 4.1/5 (96 download)

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Book Synopsis Lectures on Curves, Surfaces and Projective Varieties by : Mauro Beltrametti

Download or read book Lectures on Curves, Surfaces and Projective Varieties written by Mauro Beltrametti and published by European Mathematical Society. This book was released on 2009 with total page 512 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers a wide-ranging introduction to algebraic geometry along classical lines. It consists of lectures on topics in classical algebraic geometry, including the basic properties of projective algebraic varieties, linear systems of hypersurfaces, algebraic curves (with special emphasis on rational curves), linear series on algebraic curves, Cremona transformations, rational surfaces, and notable examples of special varieties like the Segre, Grassmann, and Veronese varieties. An integral part and special feature of the presentation is the inclusion of many exercises, not easy to find in the literature and almost all with complete solutions. The text is aimed at students in the last two years of an undergraduate program in mathematics. It contains some rather advanced topics suitable for specialized courses at the advanced undergraduate or beginning graduate level, as well as interesting topics for a senior thesis. The prerequisites have been deliberately limited to basic elements of projective geometry and abstract algebra. Thus, for example, some knowledge of the geometry of subspaces and properties of fields is assumed. The book will be welcomed by teachers and students of algebraic geometry who are seeking a clear and panoramic path leading from the basic facts about linear subspaces, conics and quadrics to a systematic discussion of classical algebraic varieties and the tools needed to study them. The text provides a solid foundation for approaching more advanced and abstract literature.

Methods of Algebraic Geometry in Control Theory: Part II

Author : Peter Falb
Publisher : Springer Science & Business Media
ISBN 13 : 1461215641
Total Pages : 382 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Methods of Algebraic Geometry in Control Theory: Part II by : Peter Falb

Download or read book Methods of Algebraic Geometry in Control Theory: Part II written by Peter Falb and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 382 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Control theory represents an attempt to codify, in mathematical terms, the principles and techniques used in the analysis and design of control systems. Algebraic geometry may, in an elementary way, be viewed as the study of the structure and properties of the solutions of systems of algebraic equations. The aim of this book is to provide access to the methods of algebraic geometry for engineers and applied scientists through the motivated context of control theory" .* The development which culminated with this volume began over twenty-five years ago with a series of lectures at the control group of the Lund Institute of Technology in Sweden. I have sought throughout to strive for clarity, often using constructive methods and giving several proofs of a particular result as well as many examples. The first volume dealt with the simplest control systems (i.e., single input, single output linear time-invariant systems) and with the simplest algebraic geometry (i.e., affine algebraic geometry). While this is quite satisfactory and natural for scalar systems, the study of multi-input, multi-output linear time invariant control systems requires projective algebraic geometry. Thus, this second volume deals with multi-variable linear systems and pro jective algebraic geometry. The results are deeper and less transparent, but are also quite essential to an understanding of linear control theory. A review of * From the Preface to Part 1. viii Preface the scalar theory is included along with a brief summary of affine algebraic geometry (Appendix E).

Geometrical Methods for the Theory of Linear Systems

Author : C.I. Byrnes
Publisher : Springer Science & Business Media
ISBN 13 : 9400990820
Total Pages : 320 pages
Book Rating : 4.4/5 (9 download)

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Book Synopsis Geometrical Methods for the Theory of Linear Systems by : C.I. Byrnes

Download or read book Geometrical Methods for the Theory of Linear Systems written by C.I. Byrnes and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: The lectures contained in this book were presented at Harvard University in June 1979. The workshop at which they were presented was the third such on algebro-geometric methods. The first was held in 1973 in London and the emphasis was largely on geometric methods. The second was held at Ames Research Center-NASA in 1976. There again the emphasis was on geometric methods, but algebraic geometry was becoming a dominant theme. In the two years after the Ames meeting there was tremendous growth in the applications of algebraic geometry to systems theory and it was becoming clear that much of the algebraic systems theory was very closely related to the geometric systems theory. On this basis we felt that this was the right time to devote a workshop to the applications of algebra and algebraic geometry to linear systems theory. The lectures contained in this volume represent all but one of the tutorial lectures presented at the workshop. The lec ture of Professor Murray Wonham is not contained in this volume and we refer the interested to the archival literature. This workshop was jointly sponsored by a grant from Ames Research Center-NASA and a grant from the Advanced Study Institute Program of NATO. We greatly appreciate the financial support rendered by these two organizations. The American Mathematical Society hosted this meeting as part of their Summer Seminars in Applied Mathematics and will publish the companion volume of con tributed papers.

Classical Algebraic Geometry

Author : Igor V. Dolgachev
Publisher : Cambridge University Press
ISBN 13 : 1139560786
Total Pages : 653 pages
Book Rating : 4.1/5 (395 download)

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Book Synopsis Classical Algebraic Geometry by : Igor V. Dolgachev

Download or read book Classical Algebraic Geometry written by Igor V. Dolgachev and published by Cambridge University Press. This book was released on 2012-08-16 with total page 653 pages. Available in PDF, EPUB and Kindle. Book excerpt: Algebraic geometry has benefited enormously from the powerful general machinery developed in the latter half of the twentieth century. The cost has been that much of the research of previous generations is in a language unintelligible to modern workers, in particular, the rich legacy of classical algebraic geometry, such as plane algebraic curves of low degree, special algebraic surfaces, theta functions, Cremona transformations, the theory of apolarity and the geometry of lines in projective spaces. The author's contemporary approach makes this legacy accessible to modern algebraic geometers and to others who are interested in applying classical results. The vast bibliography of over 600 references is complemented by an array of exercises that extend or exemplify results given in the book.

Observability and Controllability of General Linear Systems

Author : Lyubomir T. Gruyitch
Publisher : CRC Press
ISBN 13 : 042977852X
Total Pages : 326 pages
Book Rating : 4.4/5 (297 download)

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Book Synopsis Observability and Controllability of General Linear Systems by : Lyubomir T. Gruyitch

Download or read book Observability and Controllability of General Linear Systems written by Lyubomir T. Gruyitch and published by CRC Press. This book was released on 2018-10-31 with total page 326 pages. Available in PDF, EPUB and Kindle. Book excerpt: Observability and Controllability of General Linear Systems treats five different families of the linear systems, three of which are new. The book begins with the definition of time together with a brief description of its crucial properties. It presents further new results on matrices, on polynomial matrices, on matrix polynomials, on rational matrices, and on the new compact, simple and elegant calculus that enabled the generalization of the transfer function matrix concept and of the state concept, the proofs of the new necessary and sufficient observability and controllability conditions for all five classes of the studied systems. Features • Generalizes the state space concept and the complex domain fundamentals of the control systems unknown in previously published books by other authors. • Addresses the knowledge and ability necessary to overcome the crucial lacunae of the existing control theory and drawbacks of its applications. • Outlines new effective mathematical means for effective complete analysis and synthesis of the control systems. • Upgrades, completes and broadens the control theory related to the classical self-contained control concepts: observability and controllability. • Provides information necessary to create and teach advanced inherently upgraded control courses.

Trackability and Tracking of General Linear Systems

Author : Lyubomir T. Gruyitch
Publisher : CRC Press
ISBN 13 : 0429778104
Total Pages : 380 pages
Book Rating : 4.4/5 (297 download)

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Book Synopsis Trackability and Tracking of General Linear Systems by : Lyubomir T. Gruyitch

Download or read book Trackability and Tracking of General Linear Systems written by Lyubomir T. Gruyitch and published by CRC Press. This book was released on 2018-10-31 with total page 380 pages. Available in PDF, EPUB and Kindle. Book excerpt: Trackability and Tracking of General Linear Systems deals with five classes of the systems, three of which are new, begins with the definition of time together with a brief description of its crucial properties and with the principles of the physical uniqueness and continuity of physical variables. They are essential for the natural tracking control synthesis. The book presents further new results on the new compact, simple and elegant calculus that enabled the generalization of the transfer function matrix concept and of the state concept, the completion of the trackability and tracking concepts together with the proofs of the trackability and tracking criteria, as well as the natural tracking control synthesis for all five classes of the systems. Features • Crucially broadens the state space concept and the complex domain fundamentals of the dynamical systems to the control systems. • Addresses the knowledge and ability necessary to study and design control systems that will satisfy the fundamental control goal. • Outlines new effective mathematical means for effective complete analysis and synthesis of the control systems. • Upgrades, completes and essentially generalizes the control theory beyond the existing boundaries. • Provides information necessary to create and teach advanced inherently upgraded control courses.

Three Decades of Progress in Control Sciences

Author : Xiaoming Hu
Publisher : Springer Science & Business Media
ISBN 13 : 3642112781
Total Pages : 376 pages
Book Rating : 4.6/5 (421 download)

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Book Synopsis Three Decades of Progress in Control Sciences by : Xiaoming Hu

Download or read book Three Decades of Progress in Control Sciences written by Xiaoming Hu and published by Springer Science & Business Media. This book was released on 2010-10-29 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this edited collection we commemorate the 60th birthday of Prof. Christopher Byrnes and the retirement of Prof. Anders Lindquist from the Chair of Optimization and Systems Theory at KTH. These papers were presented in part at a 2009 workshop in KTH, Stockholm, honoring the lifetime contributions of Professors Byrnes and Lindquist in various fields of applied mathematics.

Structural Methods in the Study of Complex Systems

Author : Elena Zattoni
Publisher : Springer
ISBN 13 : 3030185729
Total Pages : 279 pages
Book Rating : 4.0/5 (31 download)

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Book Synopsis Structural Methods in the Study of Complex Systems by : Elena Zattoni

Download or read book Structural Methods in the Study of Complex Systems written by Elena Zattoni and published by Springer. This book was released on 2019-06-27 with total page 279 pages. Available in PDF, EPUB and Kindle. Book excerpt: Structural Methods in the Study of Complex Systems helps the reader respond to the challenge of mastering complexity in systems and control. The book details the fundamental control problems arising from complex dynamical systems and shows how they can be tackled effectively by means of methods developed from graph theory, differential algebra and geometric approaches. These “structural methods” produce abstractions that fit a wide variety of applications by taking advantage of their intrinsic focus on the essential characteristics of dynamical systems, their geometric perspective and visual representation, and their algebraic formalization and ability to generate algorithmic frameworks to complement the theoretical treatment. The original work and latest achievements of the contributors, expanding on material presented at a workshop organized to coincide with the 2018 European Control Conference will assist systems and control scientists interested in developing theoretical and computational tools to solve analysis and synthesis problems involving complex dynamical systems. The contributions provide a comprehensive picture of available results along with a stimulating view of possible directions for future investigations in the field. Emphasis is placed on methods with solid computational background and on specific engineering applications so that readers from both theoretical and practical backgrounds will find this collection of use.

Linear Algebra and Projective Geometry

Author : Reinhold Baer
Publisher : Courier Corporation
ISBN 13 : 0486154661
Total Pages : 338 pages
Book Rating : 4.4/5 (861 download)

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Book Synopsis Linear Algebra and Projective Geometry by : Reinhold Baer

Download or read book Linear Algebra and Projective Geometry written by Reinhold Baer and published by Courier Corporation. This book was released on 2012-06-11 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: Geared toward upper-level undergraduates and graduate students, this text establishes that projective geometry and linear algebra are essentially identical. The supporting evidence consists of theorems offering an algebraic demonstration of certain geometric concepts. 1952 edition.

Introduction to Non-linear Algebra

Author : Valeri? Valer?evich Dolotin
Publisher : World Scientific
ISBN 13 : 9812708006
Total Pages : 286 pages
Book Rating : 4.8/5 (127 download)

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Book Synopsis Introduction to Non-linear Algebra by : Valeri? Valer?evich Dolotin

Download or read book Introduction to Non-linear Algebra written by Valeri? Valer?evich Dolotin and published by World Scientific. This book was released on 2007 with total page 286 pages. Available in PDF, EPUB and Kindle. Book excerpt: Literaturverz. S. 267 - 269

Selected Topics in Algebraic Geometry

Author : National Research Council (U.S.). Committee on Rational Transformations
Publisher : American Mathematical Soc.
ISBN 13 : 9780828401890
Total Pages : 518 pages
Book Rating : 4.4/5 (18 download)

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Book Synopsis Selected Topics in Algebraic Geometry by : National Research Council (U.S.). Committee on Rational Transformations

Download or read book Selected Topics in Algebraic Geometry written by National Research Council (U.S.). Committee on Rational Transformations and published by American Mathematical Soc.. This book was released on 1970 with total page 518 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book resulted from two reports (published in 1928 and 1932) of the Committee on Rational Transformations, established by the National Research Council. The purpose of the reports was to give a comprehensive survey of the literature on the subject. Each chapter is regarded as a separate unit that can be read independently.